Suppose that the freely falling object in the exercise 1 were also equipped with an odometer. Would the readings of distance fallen each second indicate equal or different falling distances for successive seconds? Exercise 1 Suppose that a freely falling object were somehow equipped with a speedometer. By how much would its reading in speed increase with each second of fall?
ANSWER: When the objects falls freely under gravity, it obeys the specific equation of motion about it’s speed and distance. Let’s first do it for the distance, which obeys the equation, STEP 1:- S = ut + 1/2 at = 1/2 gt = 1/2 × 9.8 × t . Here in the above equation, the acceleration is the acceleration due to gravity because there is only the force of gravity acts on the object. We have considered the object released from zero speed, so the 1st term in the equation gets canceled. Finally the distance travelled increases as the square of time. So, with each passing second, the distance increases a lot. In each successive second the object covered has more and more distance. As the odometer shows the distance travelled, the readings will be different (with increasing order). STEP 2:- For the velocity, we are going to use this equation of motion, V = u + at = 0 + gt = 9.8 × t Again in the above equation, we have considered the initial velocity was zero, as the object released from zero speed and the acceleration is the acceleration due to gravity. a = g = 9.8 m/s . As we got the velocity as 9.8 × t, The speed after the 1st second will be, 9.8 × 1 = 9.8 m/s. The speed after 2 seconds will be, 9.8 × 2 = 19.6 m/s. CONCLUSION:- So after each second, the speed increases by 9.8 m/s.